The Internet of Things and the Wireless Sensor Networks are providing new ways to connect physical variables from the environment to the cybernetic world. As their applications become more ubiquitous, they require better energy efficiency to reduce the size of the batteries or extend their lifetime as much as possible, while keeping good quality network performance. Traditional solutions to this challenge have used a duty-cycle approach at the medium access control layer of the communication stack trading off latency for energy efficiency. Wake-up radios is a new technology for wireless communications that promises the end of this tradeoff thanks to its ultra-low power consumption. This module is attached to a regular node as a secondary receiver that listens to the channel continuously while the main radio stays sleeping. Unfortunately, the sensitivity of the wake-up receiver is very low creating a range mismatch with the main radio. This leads to very dense networks according to the very short range of the wake-up radio. In such a scenario, the data frame must pass through every node in the path from source to destination, wasting the benefits of the main radio technology. To take advantage of the full range of the main radio, the signals on the wake-up radio have to be routed through intermediate nodes before waking up the destination, so that the data can be sent directly from source to destination. In this article, we present REFLOOD, a reactive routing protocol for WuR networks that tackles this challenge taking advantage of multiple paths and achieving load balancing. We compare it with a proactive approach as well as a traditional solution in ContikiOS, through simulations in different scenarios for convergecast traffic. The results show that REFLOOD represents an improvement to 300% of the network lifetime of traditional solutions. Its multi-path feature maximizes the chances to wake-up a destination successfully, improving the packet delivery ratio, and reducing the latency.